Wireless power systems having interleaved rectifiers

ABSTRACT

A wireless power receiver is coupled to an impedance matching network, the impedance matching network having a first node and a second node. Coupled to the first node is a first branch having a first positive reactance and a second branch having a first negative reactance, wherein an absolute value of the first positive reactance is different from an absolute value of the first negative reactance, and coupled to the second node is a third branch having a second positive reactance and a fourth branch having a second negative reactance, wherein an absolute value of the second positive reactance is different from an absolute value of the second negative reactance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/685,889, filed Aug. 24, 2017, entitled “Wireless power systems havinginterleaved rectifiers,” which claims priority to U.S. ProvisionalPatent Application No. 62/379,042, filed Aug. 24, 2016, entitled,“Wireless power receivers having interleaved rectifiers,” and U.S.Provisional Patent Application No. 62/412,595, filed Oct. 25, 2016,entitled, “Wireless power receivers having interleaved rectifiers,” thedisclosures of which are incorporated herein, in their entirety, byreference.

TECHNICAL FIELD

The disclosure generally relates to wireless power systems and, moreparticularly, the disclosure relates to rectifiers for wireless powerreceivers in wireless power systems.

BACKGROUND

Wireless power systems can be used to charge batteries having largevoltage ranges. A major challenge in efficiently transmitting power froma wireless power transmitter to a receiver is the range of impedancesthat need to be matched to respond to the large voltage range. Further,in practical wireless power systems, there is a significant amount ofharmonic content related to the fundamental frequency of the oscillatingenergy in the receiver of the wireless power system.

SUMMARY

In accordance with one embodiment, a wireless power receiver includes areceiver resonator coupled to an impedance matching network, theimpedance matching network having a first node and a second node.Coupled to the first node is a first branch having a first positivereactance and a second branch having a first negative reactance, whereinan absolute value of the first positive reactance is different from anabsolute value of the first negative reactance, and coupled to thesecond node is a third branch having a second positive reactance and afourth branch having a second negative reactance, wherein an absolutevalue of the second positive reactance is different from an absolutevalue of the second negative reactance. The receiver further includes afirst rectifier having a first rectifier input coupled to the firstbranch, a second rectifier having a second rectifier input coupled tothe second branch, a third rectifier having a third rectifier inputcoupled to the third branch, and a fourth rectifier having a fourthrectifier input coupled to the fourth branch.

In a related embodiment, the absolute value of the first negativereactance is at least 4% different than the absolute value of the firstpositive reactance and the absolute value of the second negativereactance is at least 4% different than the absolute value of the secondpositive reactance. Optionally, the absolute value of the first negativereactance is at least 10% different than the absolute value of the firstpositive reactance and the absolute value of the second negativereactance is at least 10% different than the absolute value of thesecond positive reactance. Optionally, the absolute value of the firstnegative reactance is at least 20% different than the absolute value ofthe first positive reactance and the absolute value of the secondnegative reactance is at least 20% different than of the absolute valueof the second positive reactance.

In another related embodiment, during reception of electromagneticenergy by the wireless power receiver, a first current is formed in thefirst branch and a second current is formed in the second branch,wherein a magnitude of the first current is within 30% of a magnitude ofthe second current, and a third current is formed in the third branchand a fourth current is formed in the fourth branch, wherein a magnitudeof the third current is within 30% of a magnitude of the fourth current,each of the currents oscillating at a fundamental frequency f₀ and atleast one harmonic frequency f_(h) of the fundamental frequency.

In yet another related embodiment, the receiver is configured to deliverpower to a battery with a voltage range V_(low) to V_(high), the batterycoupled to an output of the first and second rectifiers, and forvoltages V_(low) to 0.5(V_(low)+V_(high)), (i) a magnitude of the firstcurrent is within 30% of a magnitude of the second current and (ii) amagnitude of the third current is within 30% of a magnitude of thefourth current. Optionally, the wireless power receiver of claim 4wherein, for voltage V_(low), the magnitude of the first current iswithin 10% of the magnitude of the second current and the magnitude ofthe third current is within 10% of the magnitude of the fourth current.

In a related embodiment, each rectifier has a positive output and anegative output, the positive outputs of the rectifiers joined to form afirst output node and the negative outputs of the rectifiers are joinedto form a second output node. Optionally, the first output node andsecond output node are coupled to a single load. In another relatedembodiment, the first output node and the second output node are coupledto a smoothing capacitor, the smoothing capacitor configured to becoupled in parallel with a load.

In another related embodiment, the impedance matching network includes afirst tunable element coupled to the first node and a second tunableelement coupled to the second node, so that the wireless power receivercan accommodate a range of the fundamental frequency f₀. Optionally, thefirst tunable element and second tunable element each comprise a tunablecapacitor.

In a related embodiment, each of the first, second, third, and fourthrectifiers is a half bridge rectifier. Optionally, the first rectifierand the third rectifier are coupled to form a full bridge rectifier, andthe second and fourth rectifiers are coupled to form a full bridgerectifier. Optionally, the first, second, third, and fourth rectifiersare either diode rectifiers or switching rectifiers.

In another related embodiment, the first branch and the third brancheach comprise a first inductor and a first capacitor, an absolute valueof a reactance value of the first inductor being greater than anabsolute value of a reactance value of first capacitance. Optionally,the second branch and the fourth branch each comprise a second inductorand a second capacitor, an absolute value of a reactance value of thesecond inductor being less than an absolute value of a reactance valueof the second capacitor.

In yet another related embodiment, an inductance value of the firstinductor is approximately equal to an inductance value of the secondinductor. Optionally, the fundamental frequency f₀ is 85 kHz.Optionally, or alternatively, the fundamental frequency f₀ is 6.78 MHz.

In accordance with another embodiment, a vehicle charging systemincludes a wireless power receiver having a receiver resonator coupledto an impedance matching network, the impedance matching network havinga first node and a second node. Coupled to the first node is a firstbranch having a first positive reactance and a second branch comprisinga first negative reactance, wherein an absolute value of the firstpositive reactance is different from an absolute value of the firstnegative reactance, and coupled to the second node is a third branchhaving a second positive reactance and a fourth branch having a secondnegative reactance, wherein an absolute value of the second positivereactance is different from an absolute value of the second negativereactance. The receiver further includes a first rectifier having afirst rectifier input coupled to the first branch, a second rectifierhaving a second rectifier input coupled to the second branch, a thirdrectifier having a third rectifier input coupled to the third branch,and a fourth rectifier having a fourth rectifier input coupled to thefourth branch. The vehicle charger system further includes a vehiclebattery coupled to a first output node and a second output node, thefirst output node formed from an output of the first rectifier and anoutput of the third rectifier and the second output node is formed froman output of the second rectifier and an output of the fourth rectifier.

In a related embodiment, the absolute value of the first negativereactance is at least 4% different than the absolute value of the firstpositive reactance and the absolute value of the second negativereactance is at least 4% different than the absolute value of the secondpositive reactance. Optionally, the absolute value of the first negativereactance is at least 10% different than the absolute value of the firstpositive reactance and the absolute value of the second negativereactance is at least 10% different than the absolute value of thesecond positive reactance. Optionally, the absolute value of the firstnegative reactance is at least 20% different than the absolute value ofthe first positive reactance and the absolute value of the secondnegative reactance is at least 20% different than of the absolute valueof the second positive reactance.

In another related embodiment, during reception of electromagneticenergy by the wireless power receiver, a first current is formed in thefirst branch and a second current is formed in the second branch,wherein a magnitude of the first current is within 30% of a magnitude ofthe second current, and a third current is formed in the third branchand a fourth current is formed in the fourth branch, wherein a magnitudeof the third current is within 30% of a magnitude of the fourth current,each of the currents oscillating at a fundamental frequency f₀ and atleast one harmonic frequency f_(h) of the fundamental frequency.

In yet another related embodiment, the receiver is configured to deliverpower to a battery with a voltage range V_(low) to V_(high), the batterycoupled to an output of the first and second rectifiers, and forvoltages V_(low) to 0.5(V_(low)+V_(high)), (i) a magnitude of the firstcurrent is within 30% of a magnitude of the second current and (ii) amagnitude of the third current is within 30% of a magnitude of thefourth current. Optionally, the wireless power receiver of claim 4wherein, for voltage V_(low), the magnitude of the first current iswithin 10% of the magnitude of the second current and the magnitude ofthe third current is within 10% of the magnitude of the fourth current.

In a related embodiment, each rectifier has a positive output and anegative output, the positive outputs of the rectifiers joined to form afirst output node and the negative outputs of the rectifiers are joinedto form a second output node. Optionally, the first output node andsecond output node are coupled to a single load. In another relatedembodiment, the first output node and the second output node are coupledto a smoothing capacitor, the smoothing capacitor configured to becoupled in parallel with a load.

In another related embodiment, the impedance matching network includes afirst tunable element coupled to the first node and a second tunableelement coupled to the second node, so that the wireless power receivercan accommodate a range of the fundamental frequency f₀. Optionally, thefirst tunable element and second tunable element each comprise a tunablecapacitor.

In a related embodiment, each of the first, second, third, and fourthrectifiers is a half bridge rectifier. Optionally, the first rectifierand the third rectifier are coupled to form a full bridge rectifier, andthe second and fourth rectifiers are coupled to form a full bridgerectifier. Optionally, the first, second, third, and fourth rectifiersare either diode rectifiers or switching rectifiers.

In another related embodiment, the first branch and the third brancheach comprise a first inductor and a first capacitor, an absolute valueof a reactance value of the first inductor being greater than anabsolute value of a reactance value of first capacitance. Optionally,the second branch and the fourth branch each comprise a second inductorand a second capacitor, an absolute value of a reactance value of thesecond inductor being less than an absolute value of a reactance valueof the second capacitor.

In yet another related embodiment, an inductance value of the firstinductor is approximately equal to an inductance value of the secondinductor. Optionally, the fundamental frequency f₀ is 85 kHz.Optionally, or alternatively, the fundamental frequency f₀ is 6.78 MHz.

BRIEF DESCRIPTION OF THE DRAWINGS

Those skilled in the art should more fully appreciate advantages ofvarious embodiments from the following “Detailed Description,” discussedwith reference to the drawings summarized immediately below.

FIG. 1 is a diagram of an exemplary wireless power system including awireless power receiver having an interleaved rectifier.

FIG. 2 is a diagram of an exemplary circuit implementation of a wirelesspower receiver having an interleaved rectifier.

FIG. 3 is a schematic of an exemplary circuit implementation of awireless power receiver having an interleaved rectifier.

FIG. 4 is a schematic of an exemplary embodiment of a portion of awireless power receiver having an interleaved rectifier. FIG. 5A is adiagram of an exemplary embodiment of integrated inductors that can beused for two or more of inductors L4A, L4B, L4C, and L4D in the matchingnetwork of the wireless power receiver. FIG. 5B is a diagram of anexemplary embodiment of integrated inductors that can be used for thefour inductors L4A, L4C, L4B, and L4D in the matching network of thewireless power receiver.

FIG. 6A is a plot of current levels in an impedance matching networkhaving uncompensated reactance in an exemplary wireless power receiver.FIG. 6B is a plot of current levels in an impedance matching networkhaving compensated reactance in an exemplary wireless power receiver.

FIG. 7A is a plot of input resistance R_(in) as a function of batteryvoltage V_(batt) for receivers having various configurations ofuncompensated and compensated reactances.

FIG. 7B is a plot of input reactance X_(in) as a function of batteryvoltage V_(batt). FIG. 7C is a plot of input resistance R_(in) as afunction of battery voltage V_(batt) for receivers having variousconfigurations of uncompensated and compensated reactances. FIG. 7D is aplot of input reactance X_(in) as a function of battery voltageV_(batt).

DETAILED DESCRIPTION

In illustrative embodiments, wireless power systems include receivershaving interleaved rectifiers. Further, these wireless power receiversinclude components that efficiently couple energy from a receivingelement to the load. A rectifier is typically required for loadsrequiring direct current or constant voltage. Interleaved rectifiers canhave multiple benefits in wireless power systems, as detailed below.Some of these benefits include (i) the reduction of the range of loadimpedances that a wireless power system experiences; (ii) improvement toefficiency at full and reduced power levels transmitted by the wirelesspower transmitter; (iii) easier system control when the transmitter isdetuned; (iv) maintenance or reduction in footprint of components inwireless power system as compared to those without; (v) improvement toefficiency over a wide range of battery voltages; and/or (vi) reductionof stress on rectifier components. Details of illustrative embodimentsare discussed below.

FIG. 1 shows a high level functional block diagram of an exemplaryembodiment of a wireless power system 100 including a wireless powerreceiver having an interleaved rectifier, as described more fully below.Input power to the system can be provided by wall power (AC mains), forexample, which is converted to DC in an AC/DC converter block 102.Alternatively, a DC voltage can be provided directly from a battery orother DC supply. In some embodiments, the AC/DC converter block 102 maybe a power factor correction (PFC) stage. The PFC, in addition toconverting the AC input (for example, at 50 or 60 Hz) to DC, cancondition the current such that the current is substantially in phasewith the voltage. A high-efficiency switching inverter or amplifier 104converts the DC voltage into an AC voltage waveform used to drive atransmitter resonator 106. In some embodiments, the frequency of the ACvoltage waveform may be in the range of 80 to 90 kHz. In someembodiments, the frequency of the AC voltage waveform may be in therange of 10 kHz to 15 MHz. In one particular embodiment, the frequencyof the AC voltage waveform is about 6.78 MHz that may vary within a 15kHz band due to FCC and CISPR regulations. These exemplary frequenciesmay be termed as an “operating frequency” of the wireless power system.

In the exemplary system 100, a transmitter impedance matching network(Tx IMN) 108 efficiently couples the inverter 104 output to thetransmitter resonator 106 and can enable efficient switching-amplifieroperation. Class D or E switching amplifiers are suitable in manyapplications and can require an inductive load impedance for highestefficiency. The Tx IMN 108 transforms the transmitter resonatorimpedance into such an impedance for the inverter 104. The transmitterresonator impedance can be, for example, loaded by coupling to areceiver resonator 110 and/or output load. The magnetic field generatedby the transmitter resonator 106 couples to the receiver resonator 110,thereby inducing a voltage in receiver resonator 110. This energy can becoupled out of the receiver resonator 110 to, for example, directlypower a load or charge a battery. A receiver impedance matching network(IMN) 112 can be used to efficiently couple energy from the receiverresonator 110 to a load 114 and optimize power transfer betweentransmitter resonator 106 and receiver resonator 110. It may transformthe actual load impedance into an effective load impedance seen by thereceiver resonator 110 which more closely matches the loading foroptimum efficiency. For loads requiring direct current or constantvoltage (also known as DC voltage), a rectifier 116 converts thereceived AC power into DC. In embodiments, the transmitter 118 andreceiver 120 can each further include filters, sensors, and othercomponents.

The impedance matching networks (IMNs) 108, 112 can be designed tomaximize the power delivered to the load 114 at a desired frequency(e.g., 80-90 kHz, 100-200 kHz, 6.78 MHz) or to maximize power transferefficiency. The impedance matching components in the IMNs 108, 112 canbe chosen and connected so as to preserve a high-quality factor (Q)value of resonators 106, 110.

The IMNs' (108, 112) components can include, for example, a capacitor ornetworks of capacitors, an inductor or networks of inductors, or variouscombinations of capacitors, inductors, diodes, switches, and resistors.The components of the IMNs can be adjustable and/or variable and can becontrolled to affect the efficiency and operating point of the system.Impedance matching can be modified by varying capacitance, varyinginductance, controlling the connection point of the resonator, adjustingthe permeability of a magnetic material, controlling a bias field,adjusting the frequency of excitation, and the like. It is understoodthat a system with fixed matching (e.g., fixed inductance, capacitance,etc.) with fixed frequency, fixed input voltage, etc., can achieveimpedance matching at some operating conditions. Varying frequency,input voltage, or components' effective value can change the matchingand/or the output. The impedance matching can use or include any numberor combination of varactors, varactor arrays, switched elements,capacitor banks, switched and tunable elements, reverse bias diodes, airgap capacitors, compression capacitors, barium zirconium titanate (BZT)electrically tuned capacitors, microelectromechanical systems(MEMS)-tunable capacitors, voltage variable dielectrics, transformercoupled tuning circuits, and the like. The variable components can bemechanically tuned, thermally tuned, electrically tuned,piezo-electrically tuned, and the like. Elements of the impedancematching can be silicon devices, gallium nitride devices, siliconcarbide devices, and the like. The elements can be chosen to withstandhigh currents, high voltages, high powers, or any combination ofcurrent, voltage, and power. The elements can be chosen to be high-Qelements.

It is understood that the transmitter and/or receiver impedance matchingnetworks (IMNs) can have a wide range of circuit implementations withvarious components having impedances to meet the needs of a particularapplication. U.S. Pat. No. 8,461,719 to Kesler et al., which isincorporated herein by reference, discloses a variety of tunableimpedance networks, such as in FIGS. 28a-37b , for example. It isfurther understood that any practical number of switched capacitors canbe used on the source and/or device side to provide desired operatingcharacteristics.

FIG. 2 shows a block diagram of an exemplary embodiment of a wirelesspower receiver having an interleaved rectifier. The receiver includes aresonator 110 coupled to an impedance matching network (IMN) havingbalanced electronic components 202A, 202B. In some embodiments, theseelectronic components 202A, 202B can include tunable capacitors and/orinductors. These components are connected to a first stage 204 of theinterleaved rectifier having balanced electronic components.

Balancing components can be important to reject any common-mode signalthat may be present due to, for example, perturbations of drivingcircuitry. Note that each of the top branches (204A and 204C) haspositive reactance+jX₁ and +jX₃ and each of the bottom branches (204Band 204D) has negative reactance −jX₂ and −jX₄. The positive reactance+jX (−jX₁, +jX₃) branches 204A, 204C of the first stage 204 areconnected to a first rectifier 206A of the second stage 206 of theinterleaved rectifier. The negative reactance −jX (−jX₂, −jX₄) branches204B, 204D of the second stage 204 are connected to a second rectifier206B of the second stage 206 of the interleaved rectifier. Note that, insome embodiments, the absolute value of positive and negative reactancevalues may be equal to one another. In other embodiments, the absolutevalue of the positive reactance may be greater or less than the absolutevalue of the negative reactance. The outputs of these rectifiers 206A,206B are added together, as more fully described below, to connect tothe load 114, such as a battery or battery manager. Note that an effectof the “interleaved rectification” is the advantageous recombining ofrectified signals that can potentially be out of phase with respect toone another. This can lead to a smoothing effect on the combined signaloutput.

In some exemplary wireless power systems, a switching inverter 104 cangenerate an alternating current or oscillating voltage at one or moreharmonic frequencies f_(h) of the fundamental frequency f₀, in additionto the fundamental frequency f₀ itself. Energy at one or more harmonicfrequencies f_(h), in addition to the fundamental frequency f₀,propagates from the transmitter to the receiver. For example, for anoperating frequency of 85 kHz, the current induced in the receiver bythe transmitter oscillates at frequency f₀=85 kHz and harmonicfrequencies f_(h1)=170 kHz, f_(h2)=255 kHz, f_(h3)=340 kHz, etc. In someexemplary systems, the components within the receiver can cause energyoscillating at harmonic frequencies f_(h) to propagate within thereceiver. In some embodiments, the propagation of energy at theseharmonic frequencies f_(h) (in addition to the fundamental frequency f₀)can cause the components of the receiver to behave unexpectedly ascompared to operating solely at the fundamental frequency f₀. Forexample, components such as inductors and capacitors in the receiver maybe selected to have a certain impedance during operation at thefundamental frequency f₀=85 kHz but may present significantly differentimpedance when the circuit is carrying currents at f_(h1)=170 kHz(and/or other harmonics) in addition to the fundamental frequency f₀=85kHz. Thus, it is advantageous for the components of the receiver to betuned such that the impedance in the receiver circuit is properlymatched and the transmitter is presented with an expected reflectedimpedance.

In an exemplary embodiment, to address the above challenge, the reactivecomponents can be imbalanced to mitigate an impedance mismatch due toharmonic content. In other words, the reactance X₁ of positive reactancebranch +jX₁ can be configured to differ from the reactance X₂ in thenegative reactance branch −jX₂. Hence, in the exemplary configurationshown in FIG. 2, the reactances would be configured as follows:X₁≠X₂X₃≠X₄.

In some embodiments, the difference between X₁ and X₂ may be at least 4%of the higher of X₁ and X₂. In other embodiments, the difference betweenX₁ and X₂ may be at least 1% of the higher of X₁ and X₂. In yet otherembodiments, the difference between X₁ and X₂ may be at least 5% of thehigher of X₁ and X₂. Note that these ranges can apply to the differencesbetween X₃ and X₄. In some embodiments, the difference d(X₁, X₂) betweenX₁ and X₂ is approximately the same as the difference d(X₃, X₄) betweenX₃ and X₄:d(X₁,X₂)≈d(X₃,X₄).

The unbalanced reactances lead to better balanced currents through thebranches of the receiver during the operation of the wireless powersystem. Another significant advantage to the above describedconfiguration is the reduction of the peak current in the inductorswithin the receiver, namely the inductors within the interleavedrectifier. The reduction in the peak current also mitigates any thermalissues that can arise from large currents in the inductors and/or othercomponents of the receiver.

FIG. 3 is a schematic diagram of an exemplary embodiment of a wirelesspower receiver having an interleaved rectifier. The receiver includes aninductor L1 connected in series to a capacitor C1A and capacitor C1B andconnected in parallel to a capacitor C2. Connected to each of nodes N1and N2 are fixed capacitor C3A′ connected in series to a tunablecapacitor C3A″ and fixed capacitor C3B′ connected in series to capacitorC3B″ (see examples above for tunable capacitors). Note that one or morecomponents on the top branch are balanced with one or more components ofsame or similar value on the bottom branch. For example, capacitor C1Ais balanced with capacitor C1B. Connected to node N3 is a top portion304 that includes a first branch and second branch. The first branchincludes an inductor L4A connected a capacitor C4A and a second branchincluding an inductor L4B connected to capacitor C4B. Note that theinductors and capacitors can be connected in series or parallel to oneanother. In the first branch, to achieve positive reactance, thereactance of the inductor L4A at the operating frequency may be greaterthan the reactance of capacitor C4A. In the second branch, to achievenegative reactance, the reactance of the inductor L4B at the operatingfrequency may be less than the reactance of capacitor C4B.

Connected to node N4 is bottom portion 306 that includes a third branchand a fourth branch. The third branch includes an inductor L4C connectedto capacitor C4C and a fourth branch including an inductor L4D connectedto a capacitor C4D. Note that the inductors and capacitors can beconnected in series or parallel to one another. For example, theinductor L4 connected to capacitor C4 in series creates a filter to passa current with the desired frequency to the input of the rectifier. Inthe third branch, to achieve positive reactance, the reactance of theinductor L4C at the operating frequency may be greater than thereactance of the capacitor C4C. In the fourth branch, to achievenegative reactance, the reactance of the inductor L4D at the operatingfrequency may be less than the reactance of the capacitor C4D. Note thatany of the inductors L4 and/or capacitances C4 can include tunablecomponents.

The output of first branch is connected to the input I1 of the firstrectifier Rec1 and the output of the second branch is connected to theinput 12 of Rec1. The output of the third branch is connected to theinput 13 of the second rectifier Rec2 and the output of the fourthbranch is connected to the input 14 of Rec2. Note that each of therectifiers can be a half-bridge, full-bridge, passive (diode) or active(switching) type rectifier. In embodiments, a wireless power system withan output of greater than 10, 15, 20 kW may use a switching rectifier tomaintain high efficiency of power to the load. In other words, atcertain power levels, a diode rectifier may not be able to operate asefficiently at very high power levels.

Output O3 of rectifier Rec2 is connected at node N5 such that outputs O1and O3 are electrically added. Output O4 of rectifier Rec2 is connectedat node N6 such that outputs O2 and O4 are electrically added. Combinedoutputs O1+O3 (at node N5) and O2+O4 (at node N6) are connected to asmoothing capacitor C5. Connected in parallel to the smoothing capacitorC5 is a load 114, such as a battery or battery manager. Note that theconfiguration of the rectifiers Red 1 and Rec2 are presented as two fullbridge rectifiers in FIG. 3. This two full bridge rectifierconfiguration is electrically equivalent to four half bridge rectifiersdepicted in FIG. 4. In other words, a pair (2) of half bridge rectifierscan be coupled together to form a full bridge rectifier configuration.

FIG. 4 is a diagram of an exemplary embodiment of a portion of awireless power receiver having an interleaved rectifier. The impedanceZ_(IN)=R_(IN) seen at the input of the interleaved rectifier is afunction of the load impedance Z_(DC)=R_(DC) and a characteristicimpedance, X. In the example shown in FIG. 4, reactance X_(4A)=X_(4C)=Xand X_(4B)=X_(4D)=−X The input impedance to the rectifier, as a functionof load impedance, has a minimum value when the load impedance is equalto X*(π²/8), and increases for smaller and larger load impedances. Ifthe characteristic impedance, X, is chosen such that X*(π²/8) is betweenthe minimum and maximum load impedances, for example, chosen near themidpoint, then the input impedance can vary over a smaller range thanthe output impedance. In the example, the minimum and maximum loadimpedances are denoted by the minimum and maximum battery voltagemarkers 280 V and 450 V. This is a significant benefit of theinterleaved rectifier—it can reduce the range of impedances seen by thecircuit coupled to the interleaved rectifier. Note that, in someembodiments, each of the diode configurations 402 a, 402 b, 402 c, and402 d can be operated as half-bridge rectifiers.

Below is the relationship of the input impedance as a function of loadimpedance for an ideal resistance compressor.

$R_{IN} = \frac{( {\frac{8}{\pi^{2}}R_{D\; C}} )^{2} + X^{2}}{\frac{8}{\pi^{2}}R_{D\; C}}$

For wireless power receivers that are integrated into products such asvehicles, robots, medical devices, mobile electronic devices, etc., itis highly desirable for the size, weight, or cost of the inductor(s)used in the impedance matching network to be minimized. For example, inmany applications, the inductors L4A, L4B, L4C, and L4D (see FIG. 3) maytake up a large amount of space due to the windings and magneticmaterial that make up each inductor. Thus, an inductor with a minimumpossible value is selected for each of inductors L4A, L4B, L4C, and L4D.

In some embodiments, two or more of the inductors L4A, L4B, L4C, and L4Dcan be integrated into a single structure to further minimize the size,weight, and/or cost of the integrated inductors as compared individualinductors. FIG. 5A is a diagram of an exemplary embodiment of integratedinductors that can be used for two or more of inductors L4A, L4B, L4C,and L4D in the matching network of a wireless power receiver. InductorL4A and inductor L4C share a core SC1 and share a ferrite layer SF1. Inthe illustrated embodiment, the flux generated by inductor L4A andinductor L4C is substantially cancelled in the shared ferrite layer SF1since the flow is in opposite directions. Inductor L4A and inductor L4Care additionally magnetically decoupled. Inductors L4B and L4D, whichmay share a core, have a similar configuration in which flux in a sharedferrite layer SF2 between them is substantially canceled. Inductor L4Band inductor L4D are additionally magnetically decoupled. It isunderstood that a variety of winding configurations can produce fluxcancellations to meet the needs of a particular application. FIG. 5B isa diagram of an exemplary embodiment of integrated inductors that can beused for the four inductors L4A, L4C, L4B, and L4D in the matchingnetwork of the wireless power receiver. FIG. 5B shows an exemplaryshared ferrite inductor system having four cores 502 a, 502 b, 502 c,502 d with one or more shared ferrite pieces 504 a and 504 b andcorresponding flux cancellation, as shown. It is understood that avariety of winding configurations can produce multiple fluxcancellations to meet the needs of a particular application. The fourinductors L4A, L4B, L4C, and L4D are not significantly magneticallycoupled since the shared portions of ferrite effectively prevents fluxlinked by one inductor from being linked by the other. Examples ofintegrated inductors can be found in commonly owned U.S. patentapplication Ser. No. 15/671,680 filed Aug. 8, 2017 and titled “Inductorsystem having shared material for flux cancellation”.

EXAMPLES

The following are examples that illustrate the benefits of wirelesspower receivers having compensated reactance within an interleavedrectifier. Examples 1A-1C describe embodiments of a wireless powersystem with the following specifications. The wireless power system isconfigured to transmit power of approximately 10 kW to the load at anoperating frequency of 85 kHz (the fundamental frequency f₀). Due to thesquare waveform produced by the switching inverter of the wireless powertransmitter, currents and/or voltages at frequencies other than thefundamental frequency f₀ are introduced to the system. For example,energy having at least one harmonic frequency f_(h) of the fundamentalfrequency f₀ are received by the wireless power receiver. The presenceof frequencies in the system other than the fundamental frequencyresults in impedance values other than what is expected. Note thatreactance X of the receiver is defined by the following relationship:

$X = {{\omega\; L} - \frac{1}{\omega\; C}}$

The load, in Examples 1A-1C, can be one or more batteries having anoverall voltage range V_(batt) of 280 V to 420 V.

Example 1A

For a battery voltage V_(batt) of 280 V, the following table outlinesthe values of associated with the components of an exemplary wirelesspower receiver 300. The expected impedance Z of each of the top andbottom portions 304, 306 is 6.35+j9.53 Ohms. In some embodiments, theinput voltage Vin may be adjusted to keep the input power Pin constant.

The resistances of each of the branches of the interleaved rectifier canbe determined by circuit simulations. In this particular example, theexpected resistances R_(4A), R_(4B), R_(4C), and R_(4D) are each 6.35Ohms. The expected reactances X_(4A), X_(4B), X_(4C), and X_(4D) arecalculated as follows:

$X_{4A},{X_{4C} = {{{\omega\; L} - \frac{1}{\omega\; C_{{4A},{4C}}}} = {9.53\mspace{14mu}\Omega}}}$$X_{4B},{X_{4D} = {{{\omega\; L} - \frac{1}{\omega\; C_{{4B},{4D}}}} = {{- 9.53}\mspace{14mu}\Omega}}}$

The currents I_(4A), I_(4B), I_(4C), and I_(4D) in the branches 4A, 4B,4C and 4D are measured (e.g., by a current sensor) during the operationof the wireless power system. Note that, the currents I_(4A), I_(4C)(group 1) are approximately equal (to within 1% of the larger of thecurrents) and currents I_(4B), I_(4D) (group 2) are approximately equal(to within 1% of the larger of the currents). The difference betweenthese two groups of currents, however, can be a result of the differencein the impedance Z of each branch 4A-4D. For example, in an exemplaryuncompensated system, the reactance X_(4A) is equal to reactance X_(4B)and reactance X_(4C) is equal to X_(4D). This is also termed as“uncompensated reactances”. It is uncompensated in that the reactancesare not adjusted (or imbalanced) to account for the current (and/orpower) imbalance. Thus, a uncompensated receiver having balancedreactances that receives energy at both fundamental and harmonicfrequencies experiences imbalanced currents. A compensated receiverhaving compensated reactances experiences balanced currents. In acompensated receiver, the net impedance looking into each of thebranches 4A, 4B, 4C, and 4D is similar because the physical reactancesX_(4A), X_(4B), X_(4C), and X_(4D) have been adjusted such that:X_(4A)≠X_(4B)X_(4C)≠X_(4D).

In some embodiments, these reactances X_(4A), X_(4B), X_(4C), and X_(4D)can be specifically chosen to make the net impedance looking into eachof the branches 4A, 4B, 4C, and 4D intentionally negative or positive.In some embodiments, the net impedance may be made to have a specificvalue or value range. This type of adjustment may have the benefit ofaccommodating a tunable component in the matching network (shown as 202Aor 202B in FIG. 2 or C3A″ or C3B″ in FIG. 3). For example, if thetunable component can be adjusted in one direction, namely to have morenegative or more positive reactance, then configuring the net impedanceof the interleaved rectifier in the opposite direction can provide agreater degree of adjustment for the tunable component. Examples oftunable components in wireless power systems can be found in U.S. patentapplication Ser. No. 15/422,554 filed on Feb. 2, 2017 and titled“Controlling wireless power systems” and U.S. patent application Ser.No. 15/427,186 filed on Feb. 8, 2017 and titled “PWM capacitor control”.

The percentage difference in resistance values can be calculated by thedetermining the ratio of the difference of the resistance values to thehigher of the two resistance values, as shown in the following. Thepercent difference in reactance values can be calculated by determiningthe ratio of the difference of each of the absolute values of thereactance values to the absolute value of the higher of the tworeactance values.

${\Delta\;{Resistance}},{{\Delta\; R} = \frac{( {R_{4A},R_{4C}} ) - ( {R_{4B},R_{4D}} )}{( {R_{4A},R_{4C}} )}}$${\Delta\;{Reactance}},{{\Delta\; X} = \frac{{( {X_{4A},X_{4C}} )} - {( {X_{4B},X_{4D}} )}}{{higher}\mspace{14mu}{of}\mspace{14mu}( {{( {X_{4A},X_{4C}} )},{( {X_{4B},X_{4D}} )}} )}}$

In some embodiments, the absolute value of the reactance |X_(4B)| is atleast 4% different than the absolute value of the reactance |X_(4A)| andthe absolute value of the reactance |X_(4D)| is at least 4% differentthan the absolute value of the reactance |X_(4C)|. In some embodiments,the absolute value of the reactance |X_(4B)| is at least 10% differentthan the absolute value of the reactance |X_(4A)| and the absolute valueof the reactance |X_(4D)| is at least 10% different than the absolutevalue of the reactance |X_(4C)|. In some embodiments, the absolute valueof the reactance |X_(4B)| is at least 20% different than the absolutevalue of the reactance |X_(4A)| and the absolute value of the reactance|X_(4D)| is at least 20% different than the absolute value of thereactance |X_(4C)|.

In the exemplary uncompensated receiver detailed in the table below, thedifference between the first group of currents and second group ofcurrents is approximately 20.1%:

${\Delta\;{Current}} = {\frac{( {I_{4B},I_{4D}} ) - ( {I_{4A},I_{4C}} )}{( {I_{4B},I_{4D}} )} = {0.201 = {20.1{\%.}}}}$

Note that in the above formula, the percentage difference is determinedas the difference from the higher of the currents.

In contrast, in the exemplary compensated receiver detailed in the tablebelow, the difference between the first group of currents and secondgroup of currents is approximately 0.2%:

${\Delta\;{Current}} = {\frac{( {I_{4B},I_{4D}} ) - ( {I_{4A},I_{4C}} )}{( {I_{4B},I_{4D}} )} = {0.002 = {0.2{\%.}}}}$

The imbalanced current issue present in exemplary uncompensated systemdescribed thus far has been in the context of choosing a low inductancevalue for inductors L4A-L4D. In comparison, in an exemplaryuncompensated receiver, an inductor four times the size ofminimally-sized inductor L4 may be also used to mitigate the currentimbalance. While an inductor this large may be a workable solution insome applications, in many applications, restrictions on size, cost, andweight will be major forces in commercializing a wireless powerreceiver. In some embodiments, a uncompensated receiver may requireanywhere between four to ten times the size of minimally-sized inductorL4 to reduce the current imbalance. The larger an inductor used, thebetter filtering effect it has on the currents oscillating at harmonicfrequencies. However, there is a significant challenge in reducing thesize of the inductor(s) while maintaining expected performance.

Note that, in some embodiments, inductance value L4 is the same for allof L4A, L4B, L4C, and L4D. In other words, L4=L4A=L4B=L4C=L4D.

TABLE 1 Characteristics of exemplary uncompensated and compensatedwireless power receivers configured to receive energy with fundamentalfrequency f₀ = 85 kHz, at battery voltage V_(batt) = 280 V.Uncompensated Compensated Receiver Receiver L₄ = 18.12 uH L₄ = 18.12 uHCurrents I_(4A), I_(4C) (A) 24.92 28.21 Currents I_(4B), I_(4D) (A) 31.228.26 Δ Current (%) 20.1% 0.2% Net resistance looking into 7.11 6.3branches R_(4A), _(4C) (Ohm) Net reactance looking into 10.78 9.51branches X_(4A), _(4C) (Ohm) Net resistance looking into 5.7 6.26branches R_(4B), _(4D) (Ohm) Net reactance looking into −8.61 −9.51branches X_(4B), _(4D) (Ohm) Δ Net Resistance, ΔR (%) 19.8% 0.6% Δ NetReactance, ΔX (%) 20.1%   0% Capacitances C_(4A), C_(4C) (nF) 13095 1637Capacitances C_(4B), C_(4D) (nF) 97.48 92.12 Power P_(4A) + P_(4C) (W)4414 5012 Power P_(4B) + P_(4D) (W) 5534 5002 Input Power P_(in) (W)9948 10014 Input resistance R_(in) (Ohm) 20.25 20.7 Input reactanceX_(in) (Ohm) −3.4 −0.03 Reactance X_(4A), X_(4C) (Ohm) 9.53 8.53Reactance X_(4B), X_(4D) (Ohm) −9.53 −10.65 Δ Reactance, ΔX (%)   0%19.9% 

FIG. 6A is a plot of current levels in an impedance matching networkhaving uncompensated reactance in an exemplary wireless power receiver.Line 602 a is the current magnitude for I_(4B), I_(4D) as a function oftime and line 604 a is current magnitude for I_(4A), I₄c as a functionof time. FIG. 6B is a plot of current levels in an impedance matchingnetwork having compensated reactance in an exemplary wireless powerreceiver. Line 602 b is the current magnitude for I_(4B), I_(4D) as afunction of time and line 604 b is current magnitude for I_(4A), I_(4C)as a function of time. Note that the difference 606 between themagnitude of line 602 b and the magnitude of line 604 b in FIG. 7A. Thisdifference 606 is notably absent in the current magnitudes 602 b, 604 bin FIG. 6B and serve to illustrate that the currents become balancedwhen the reactances are compensated.

Example 1B

For a battery voltage V_(batt) of 350 V, the following table outlinesthe values of associated with the components of an exemplary wirelesspower receiver 300. The expected impedance Z of the matching network is9.93+j9.53 Ohms.

Similar calculations to the previous example, Example 1A, are used hereto determine the percent difference in the current, resistance, andimpedance values. Note that the above effect of balanced currents(and/or balanced power) in the compensated receiver is less pronouncedat this battery voltage level. For example, the percent difference incurrent levels drops from 41% in a uncompensated receiver to 25.4% in acompensated receiver. A much larger inductor has the effect of reducingthe current imbalance to around 12.7% but at a much higher cost (namely,around four times the inductance value of the minimal inductance L4).

TABLE 2 Characteristics of exemplary uncompensated and compensatedwireless power receivers configured to receive energy with fundamentalfrequency f₀ = 85 kHz, at battery voltage V_(batt) = 350 V.Uncompensated Compensated Receiver Receiver L = 18.12 uH L = 18.12 uHInput voltage V_(in) (V) 316 315 Currents I_(4A), I_(4C) (A) 17.1 19.7Currents I_(4B), I_(4D) (A) 29 26.42 Δ Current (%)   41% 25.4% Netresistance looking into 12.44 10.94 branches R_(4A), _(4C) (Ohm) Netreactance looking into 13.66 11.67 branches X_(4A), _(4C) (Ohm) Netresistance looking into 7.56 8.25 branches R_(4B), _(4D) (Ohm) Netreactance looking into −7.87 −8.62 branches X_(4B), _(4D) (Ohm) Δ NetResistance, ΔR (%) 39.2% 24.6% Δ Net Reactance, ΔX (%) 42.3% 26.1%Capacitances C_(4A), C_(4C) (nF) 13095 1676 Capacitances C_(4B), C_(4D)(nF) 97.48 94.34 Power P_(4A) + P_(4C) (W) 3645 4253 Power P_(4B) +P_(4D) (W) 6355 5758 Input power P_(in) (W) 10000 10011 Input resistanceR_(in) (Ohm) 18.74 19.44 Input reactance X_(in) (Ohm) −4.88 −2.88Reactance X_(4A), X_(4C) (Ohm) 9.53 8.56 Reactance X_(4B), X_(4D) (Ohm)−9.53 −10.17 Δ Reactance, ΔX (%)   0% 15.8%

Example 1C

For a battery voltage V_(batt) of 420 V, the following table outlinesthe values of associated with the components of an exemplary wirelesspower receiver 300. The expected impedance Z of the matching network is14.3+j9.53 Ohms.

Similar calculations to Example 1A are used here to determine thepercent difference in the current, resistance, and impedance values.Note that the above effect of balanced currents (and/or balanced power)in the compensated receiver is less pronounced at this battery voltagelevel. For example, the percent difference in current levels drops from65% in a uncompensated receiver to 53.5% in a compensated receiver. Amuch larger inductor has the effect of reducing the current imbalance toaround 24.5% but at a much higher cost (namely, around four times theinductance value of the minimal inductance L4).

TABLE 3 Characteristics of exemplary uncompensated and compensatedwireless power receivers configured to receive energy with a fundamentalfrequency f₀ = 85 kHz, at battery voltage V_(batt) = 420 V.Uncompensated Compensated Receiver Receiver U = 18.12 uH U = 18.12 uHInput voltage V_(in) (V) 340 338 Currents I_(4A), I_(4C) (A) 10.5 12.72Currents I_(4B), I_(4D) (A) 29.95 27.36 Δ Current (%)   65% 53.5% Netresistance looking into 20.18 18.16 branches R_(4A), _(4C) (Ohm) Netreactance looking into 25.32 19.35 branches X_(4A), _(4C) (Ohm) Netresistance looking into 8.7 9.45 branches R_(4B), _(4D) (Ohm) Netreactance looking into −7.29 −7.94 branches X_(4B), _(4D) (Ohm) Δ NetResistance, ΔR (%) 56.9% 48.1% Δ Net Reactance, ΔX (%) 71.2% 59.0%Capacitances C_(4A), C_(4C) (nF) 13095 1676 Capacitances C_(4B), C_(4D)(nF) 97.48 94.34 Power P_(4A) + P_(4C) (W) 2224 2940 Power P_(4B) +P_(4D) (W) 7800 7073 Input power P_(in) (W) 10024 10013 Input resistanceR_(in) (Ohm) 20.22 21.1 Input reactance X_(in) (Ohm) −7.56 −5.92Reactance X_(4A), X_(4C) (Ohm) 9.53 8.56 Reactance X_(4B), X_(4D) (Ohm)−9.53 −10.17 Δ Reactance, ΔX (%)   0% 15.8%

FIG. 7A is a plot of input resistance R_(in) (see FIG. 4) as a functionof battery voltage V_(batt) and FIG. 7B is a plot of input reactanceX_(in) as a function of battery voltage V_(batt) for receivers havingvarious configurations of uncompensated and compensated reactances. Thesolid lines 702 a and 702 b represent the expected resistance andreactance, respectively, of an ideal resistance compressor in which theinput AC source (in this case, the wireless power transmitter) seesequivalent resistance of a smaller range than the equivalent loadresistance. The resistance and reactance of uncompensated (oruncompensated) receiver 704 having the minimal inductance L4=18.12 uH isrepresented in triangle shaped (▴) data points in FIGS. 7A and 7B,respectively. The resistance and reactance of compensated receiver 706having the minimal inductance L4=18.12 uH is represented in round shaped(●) data points in FIGS. 7A and 7B, respectively. As observed in theabove data, at lower battery voltages (for example, at V=280 V), boththe resistance and reactance of the compensated receiver 706 is closestto the ideal resistance compressor 702. Further, for the other batteryvoltage levels, the compensated receiver 706 is closer to the idealresistance compressor 702 than the uncompensated system 704 havingsimilar sized inductors L4. In other terms, some of the greatest benefitof the compensated receiver 706 is at the higher current levels of thereceiver.

It is possible to select the battery voltage at which the resistance andreactance of the compensated receiver 706 are closest to the idealresistance compressor 702. For example, one may select the higherbattery voltage (i.e. 420 V in this example) instead of the lowerbattery voltage (i.e. 280 V in this example) as the point at which theresistance and reactance are closest to the ideal resistance compressor.In this case, the reactance of the compensated receiver would bepositive at the lower battery voltage level.

FIG. 7C is a plot of input resistance R_(in) (see FIG. 4) as a functionof battery voltage V_(batt) and FIG. 7D is a plot of input reactanceX_(in) as a function of battery voltage V_(batt) for receiver havingcompensated reactances configured to receive energy with a fundamentalfrequency f₀=85 kHz. An exemplary compensated wireless power receivercan be designed with capacitances C_(4A), C_(4C)=445 nF, C_(4B),C_(4D)=75 nF, and inductors L4A, L4C, L4B, and L4D=18.12 uH. The solidlines 702 c and 702 d represent the expected resistance and reactance,respectively, of an ideal resistance compressor in which the input ACsource (in this case, the wireless power transmitter) sees equivalentresistance of a smaller range than the equivalent load resistance. Theresistance and reactance of compensated receiver having the minimalinductance L4=18.12 uH is represented in round shaped (●) data points inFIGS. 7C and 7D, respectively. One may select the higher battery voltage(i.e. 420 V in this example) instead of the lower battery voltage (i.e.280 V in this example) as it is the point at which the resistance andreactance are closest to the ideal resistance compressor. It isunderstood that adjustment of the elements of the receiver C3A″, C3A″(see FIG. 3) can be used to adjust the input reactance of the receiverat each of the battery voltages.

Example 2

An exemplary wireless power system is configured to operate at afundamental frequency f₀ of approximately 6.78 MHz and transmit power ofapproximately 100 W to the load. The battery voltage V_(batt) range forthis load is from 20V to 30 V. In some embodiments, the input voltageVin may be adjusted to keep the input power Pin constant. In someexemplary embodiments, the load can be a laptop or notebook computer.The following table outlines the values of associated with thecomponents of an exemplary wireless power receiver 300. The expectedimpedance Z of the matching network is 3.24+j4.86 Ohms.

The data below illustrates the benefits of compensation in reactances ofthe wireless power receiver. For example, the imbalance of the currentis reduced from 21.3% in the uncompensated receiver to 1.6% in thecompensated receiver.

TABLE 4 Characteristics of exemplary uncompensated and compensatedwireless power receivers configured to receive energy with a fundamentalfrequency f₀ = 6.78 kHz, at battery voltage V_(batt) = 20-30 V.Uncompensated Compensated receiver receiver L = 116 nH L = 116 nHCurrents I_(4A), I_(4C) (A) 3.4 3.86 Currents I_(4B), I_(4D) (A) 4.333.92 Δ Current (%) 21.3% 1.6% Net resistance looking into 3.77 3.34branches R_(4A), _(4C) (Ohm) Net reactance looking into 5.55 4.9branches X_(4A), _(4C) (Ohm) Net resistance looking into 2.98 3.27branches R_(4B), _(4D) (Ohm) Net reactance looking into −4.37 −4.82branches X_(4B), _(4D) (Ohm) Δ Net Resistance, ΔR (%)   21% 2.1% Δ NetReactance, ΔX (%) 21.3% 1.6% Capacitances C_(4A), C_(4C) (nF) 321.78 42Capacitances C_(4B), C_(4D) (nF) 2.4 2.26 Power P_(4A), P_(4C) (W) 43.849.7 Power P_(4B), P_(4D) (W) 55.6 50.32 Input Power P_(in) (W) 99.4100.02 Input resistance R_(in) (Ohm) 10.2 10.45 Input reactance X_(in)(Ohm) −1.78 −0.14 Reactance X_(4A), X_(4C) (Ohm) 4.87 4.39 ReactanceX_(4B), X_(4D) (Ohm) −4.84 −5.45 Δ Reactance, ΔX (%)  0.6% 19.4%

Note that references to any of the capacitor components described hereincan refer to one or more capacitor or capacitance componentselectrically connected to one another. In the figures, multiplecapacitor components may be represented by a single capacitor symbol forclarity.

Although the above discussion discloses various exemplary embodiments ofthe invention, it should be apparent that those skilled in the art canmake various modifications that will achieve some of the advantages ofthe invention without departing from the true scope of the disclosure.All documents referenced herein are hereby incorporated by reference.

What is claimed is:
 1. A wireless power receiver comprising: a receiverresonator coupled to an impedance matching network, the impedancematching network having a first node and a second node; coupled to thefirst node, a first branch having a first positive reactance and asecond branch having a first negative reactance; coupled to the secondnode, a third branch having a second positive reactance and a fourthbranch having a second negative reactance; a first rectifier having afirst rectifier input coupled to the first branch; a second rectifierhaving a second rectifier input coupled to the second branch; a thirdrectifier having a third rectifier input coupled to the third branch;and a fourth rectifier having a fourth rectifier input coupled to thefourth branch, such that, during reception of electromagnetic energy bythe wireless power receiver: a first current is formed in the firstbranch and a second current is formed in the second branch, wherein amagnitude of the first current is within 30% of a magnitude of thesecond current, and a third current is formed in the third branch and afourth current is formed in the fourth branch, wherein a magnitude ofthe third current is within 30% of a magnitude of the fourth current,the currents oscillating at a fundamental frequency f₀ and at least oneharmonic frequency f_(h) of the fundamental frequency f₀, wherein theabsolute value of the first negative reactance is at least 4% differentthan the absolute value of the first positive reactance and the absolutevalue of the second negative reactance is at least 4% different than theabsolute value of the second positive reactance.
 2. The wireless powerreceiver of claim 1 wherein the absolute value of the first negativereactance is at least 10% different than the absolute value of the firstpositive reactance and the absolute value of the second negativereactance is at least 10% different than the absolute value of thesecond positive reactance.
 3. A wireless power receiver comprising: areceiver resonator coupled to an impedance matching network, theimpedance matching network having a first node and a second node;coupled to the first node, a first branch having a first positivereactance and a second branch having a first negative reactance; coupledto the second node, a third branch having a second positive reactanceand a fourth branch having a second negative reactance; a firstrectifier having a first rectifier input coupled to the first branch; asecond rectifier having a second rectifier input coupled to the secondbranch; a third rectifier having a third rectifier input coupled to thethird branch; and a fourth rectifier having a fourth rectifier inputcoupled to the fourth branch, such that, during reception ofelectromagnetic energy by the wireless power receiver: a first currentis formed in the first branch and a second current is formed in thesecond branch, wherein a magnitude of the first current is within 30% ofa magnitude of the second current, and a third current is formed in thethird branch and a fourth current is formed in the fourth branch,wherein a magnitude of the third current is within 30% of a magnitude ofthe fourth current, the currents oscillating at a fundamental frequencyf₀ and at least one harmonic frequency f_(h) of the fundamentalfrequency f₀, wherein: the receiver is configured to deliver power to abattery with a voltage range V_(low) to V_(high), the battery coupled toan output of the first, second, third, and fourth rectifiers, and forvoltages V_(low) to 0.5(V_(low)+V_(high)), (i) the magnitude of thefirst current is within 30% of the magnitude of the second current and(ii) the magnitude of the third current is within 30% of the magnitudeof the fourth current.
 4. The wireless power receiver of claim 3wherein, for voltage V_(low), the magnitude of the first current iswithin 10% of the magnitude of the second current and the magnitude ofthe third current is within 10% of the magnitude of the fourth current.5. The wireless power receiver of claim 3 wherein each rectifier has apositive output and a negative output, the positive outputs of therectifiers joined to form a first output node coupled to the battery andthe negative outputs of the rectifiers joined to form a second outputnode coupled to the battery.
 6. The wireless power receiver of claim 5wherein the first output node and the second output node are coupled toa smoothing capacitor, the smoothing capacitor configured to be coupledin parallel with the battery.
 7. The wireless power receiver of claim 3wherein the impedance matching network comprises a first tunable elementcoupled to the first node and a second tunable element coupled to thesecond node.
 8. The wireless power receiver of claim 7 wherein the firsttunable element and second tunable element each comprise a tunablecapacitor.
 9. The wireless power receiver of claim 3 wherein each of thefirst, second, third, and fourth rectifiers is a half bridge rectifier.10. The wireless power receiver of claim 3 wherein the first rectifierand the third rectifier are coupled to form a full bridge rectifier, andthe second and fourth rectifiers are coupled to form a full bridgerectifier.
 11. The wireless power receiver of claim 3 wherein the first,second, third, and fourth rectifiers are either diode rectifiers orswitching rectifiers.
 12. The wireless power receiver of claim 3 whereinthe fundamental frequency f₀ is 85 kHz.
 13. A wireless power receivercomprising: a receiver resonator coupled to an impedance matchingnetwork, the impedance matching network having a first node and a secondnode; coupled to the first node, a first branch having a first positivereactance and a second branch having a first negative reactance; coupledto the second node, a third branch having a second positive reactanceand a fourth branch having a second negative reactance; a firstrectifier having a first rectifier input coupled to the first branch; asecond rectifier having a second rectifier input coupled to the secondbranch; a third rectifier having a third rectifier input coupled to thethird branch; and a fourth rectifier having a fourth rectifier inputcoupled to the fourth branch, such that, during reception ofelectromagnetic energy by the wireless power receiver: a first currentis formed in the first branch and a second current is formed in thesecond branch, wherein a magnitude of the first current is within 30% ofa magnitude of the second current, and a third current is formed in thethird branch and a fourth current is formed in the fourth branch,wherein a magnitude of the third current is within 30% of a magnitude ofthe fourth current, the currents oscillating at a fundamental frequencyf₀ and at least one harmonic frequency f_(h) of the fundamentalfrequency f₀, wherein the first branch and the third branch eachcomprise a first inductor and a first capacitor, an absolute value of areactance value of the first inductor being greater than an absolutevalue of a reactance value of the first capacitor.
 14. The wirelesspower receiver of claim 13 wherein the second branch and the fourthbranch each comprise a second inductor and a second capacitor, anabsolute value of a reactance value of the second inductor being lessthan an absolute value of a reactance value of the second capacitor. 15.The wireless power receiver of claim 14 wherein an inductance value ofthe first inductor is approximately equal to an inductance value of thesecond inductor.
 16. A vehicle charging system comprising: a wirelesspower receiver comprising: a receiver resonator coupled to an impedancematching network, the impedance matching network having a first node anda second node; coupled to the first node, a first branch having a firstpositive reactance and a second branch having a first negativereactance; coupled to the second node, a third branch having a secondpositive reactance and a fourth branch having a second negativereactance; a first rectifier having a first rectifier input coupled tothe first branch; a second rectifier having a second rectifier inputcoupled to the second branch; a third rectifier having a third rectifierinput coupled to the third branch; and a fourth rectifier having afourth rectifier input coupled to the fourth branch, such that, duringreception of electromagnetic energy by the wireless power receiver: afirst current is formed in the first branch and a second current isformed in the second branch, wherein a magnitude of the first current iswithin 30% of a magnitude of the second current, and a third current isformed in the third branch and a fourth current is formed in the fourthbranch, wherein a magnitude of the third current is within 30% of amagnitude of the fourth current, the currents oscillating at afundamental frequency f₀ and at least one harmonic frequency f_(h) ofthe fundamental frequency f₀; and a vehicle battery coupled to a firstoutput node and a second output node, the first output node formed froman output of the first rectifier and an output of the third rectifierand the second output node formed from an output of the second rectifierand an output of the fourth rectifier.
 17. The vehicle charging systemof claim 16 wherein the magnitude of the first current is within 10% ofthe magnitude of the second current and the magnitude of the thirdcurrent is within 10% of the magnitude of the fourth current.
 18. Thevehicle charging system of claim 16 wherein the absolute value of thefirst negative reactance is at least 4% different than the absolutevalue of the first positive reactance and the absolute value of thesecond negative reactance is at least 4% different than the absolutevalue of the second positive reactance.
 19. The vehicle charging systemof claim 16 wherein: the first branch and the third branch each comprisea first inductor and a first capacitor, an absolute value of a reactancevalue of the first inductor being greater than an absolute value of areactance value of the first capacitor; and the second branch and thefourth branch each comprise a second inductor and a second capacitor, anabsolute value of a reactance value of the second inductor being lessthan an absolute value of a reactance value of the second capacitor. 20.A wireless power receiver comprising: a receiver resonator coupled to animpedance matching network, the impedance matching network having afirst node and a second node; coupled to the first node, a first branchhaving a first positive reactance and a second branch having a firstnegative reactance; coupled to the second node, a third branch having asecond positive reactance and a fourth branch having a second negativereactance; a first rectifier having a first rectifier input coupled tothe first branch; a second rectifier having a second rectifier inputcoupled to the second branch; a third rectifier having a third rectifierinput coupled to the third branch; and a fourth rectifier having afourth rectifier input coupled to the fourth branch, such that, duringreception of electromagnetic energy by the wireless power receiver: afirst current is formed in the first branch and a second current isformed in the second branch, wherein a magnitude of the first current iswithin 30% of a magnitude of the second current, and a third current isformed in the third branch and a fourth current is formed in the fourthbranch, wherein a magnitude of the third current is within 30% of amagnitude of the fourth current, the currents oscillating at afundamental frequency f₀ and at least one harmonic frequency f_(h) ofthe fundamental frequency f₀, wherein a first difference between (a) anabsolute value of the first positive reactance and (b) an absolute valueof the first negative reactance is approximately equal to a seconddifference between (i) an absolute value of the second positivereactance and (ii) an absolute value of the second negative reactance.